In telecommunication systems, wherein transmission from at least one transmitting peer to at least one receiving peer is considered, knowledge of the channel between said transmitting peer and said receiving peer, can be necessary for or be used for improving the determining of the transmitted signal at the receiving peer. Said signal improving process is also denoted equalization. Said channel knowledge can be obtained by performing a channel estimation, meaning determining the frequency response of said channel.
In telecommunication methods based on subband processing one typically considers a channel with Nc carriers. Note that in subband processing of a data signal having a data rate, comprises in principle of splitting said data signal in a plurality of data signals, with a lower data rate and modulating each of said plurality of data signals with another carrier. Said carriers are preferably orthogonal. Channel estimation for channels with multiple carriers boils down to determining the channel frequency response at the frequencies of said carriers or at a subset thereof. Note that in modem wireless telecommunication methods the channel time domain response is short, thus having a finite time domain response, meaning a finite amount of non-zero samples.
An example of a modem telecommunication method is Orthogonal Frequency Division Multiplexing (OFDM), which has become increasingly popular during the last decades, mainly because it provides a substantial reduction in equalization complexity compared to classical modulation techniques. Indeed, OFDM with cyclic prefix can be equalized by a single low-rate complex multiplication on each carrier. For this reason, it has been adopted in the upcoming standards for high data-rate wireless networks, such as ETSI Hiperlan II and IEEE 802.11a. As opposed to former standards using OFDM modulation, the new standards rely on coherent QAM modulation and thus require channel estimation. Hence, the complexity of channel estimation is of crucial importance, especially for time varying channels, where this has to be performed periodically or even continuously.
Channel estimation can be performed during reception of information or data between the transmitting and receiving peer, which is denoted blind channel estimation or by transmitting specific information, also denoted reference tones, between said peers. Although the invention focuses towards non-blind channel estimation, it is clear that a combination with blind channel estimation is possible.
When relying on transmission of said specific information or reference tones, it is clear that it is beneficiary if one can estimate the channel frequency response at the frequencies of its carriers or at a subset thereof from only a limited set of reference tones, meaning less reference tones than the amount of carriers. In the context of multi-user transmission schemes, wherein each user transmits from a different transmitting peer towards at least one receiving peer, one is even obliged to use only a limited set of reference tones per user, if one wants to determining channel frequency responses of each of the users simultaneously. One can then for each user use a different set of reference tones, preferably scrambled all over the spectra of the channel. This scrambling is also denoted interleaving.
Note that as non-blind channel estimation invokes transmission of specific information, which is in fact non-useful data from a users point of view, channel estimation is considered as an overhead, which should be efficient, meaning taking a small amount of time, thus a minimal amount of reference tones, but also an efficient implementation, meaning taking a small amount of operations in order to determine the channel estimate, resulting in a fast determination and taking a small area in chip implementations. However, although complexity reduction is aimed at, still optimality of the estimation operation is an important feature.
It must be emphasized that in the modem telecommunications standards, using multi-carriers approaches, the reference tones used for channel estimation can not be chosen to be equidistant as said standards define certain carriers to be zero carriers, meaning not to be used for transmission. Indeed the standards use some zero-carriers for spectral shaping, for example, some carriers are not used to allow smooth decaying of the spectral power on the border of the bandwidth. Hence, these standards (and possible variations) will be referred to as spectral shaping systems.
Existing literature recognizes that, due to the structure of OFDM signals, the channel can be estimated by using the frequency correlation of the channel. This frequency correlation has inspired different approaches. Edfors et al. [O. Edfors, M. Sandell, J. J. van de Beek, S. K. Wilson, and P. O. Borjesson. “OFDM Channel Estimation by Singular Value Decomposition,” IEEE Trans. on Communications}, 46(7):931–939, July 1998.] use explicitly the frequency correlation and derive a linear minimum mean squared (LMMSE) estimator. Using optimal rank reduction, they develop a low complexity algorithm which computes an approximated LMMSE estimator. Complexity is here a trade-off with optimality. Raleigh and Jones [G. G. Raleigh and V. K. Jones. “Multivariate Modulation and Coding for Wireless Communication,” IEEE Journ. on Special Areas in Communications, 17(5):851–860, May 1999.] link the frequency correlation to the maximum delay spread and estimate the channel from a part of the carriers only. These carriers must be regularly spaced, which limits the application of their method.
It can be stated that prior-art channel estimation methods can not cope with non-equidistant reference or pilot tones, required by modem standard. Complexity reduction of the prior-art channel estimators leads to loss of optimality.